Spans elementary notions to the functional theory of linear integral and differential equations.Provides complete numerical algorithms for solving linear and nonlinear problems.Contains numerous Mathematica examples complete with full code and solutions.Linear Algebra and Linear Operators in Engineering is ideal as the main text of an introductory graduate course, as well as a fine instrument for self-study or as a general reference for those applying mathematics. Also included are several numerical applications, complete with Mathematica solutions and code, giving the student a "hands-on" introduction to numerical analysis. Numerous examples, problems, and illustrations highlight applications throughout engineering and the physical sciences. The result is a clear and intuitive segue to functional analysis, culminating in a practical introduction to the functional theory of integral and differential operators. Wherever possible, theorems and definitions from matrix theory are called upon to drive the analogy home. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert spaces are introduced from analogy.
Principal theorems are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and the practical application of linear algebra and functional analysis.
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